SOLUTION: 1. Create two different rational polynomial expressions with the following constraints: �one expression is undefined when x = 4, �the other is undefined when x = ‒2 or 0.

Question 1032246: 1. Create two different rational polynomial expressions with the following constraints:
�one expression is undefined when x = 4,
�the other is undefined when x = ‒2 or 0.
Then, rewrite both as equivalent expressions, with a common denominator.

2. The expression G over H is multiplied with another rational expression, and the product is 2. What is the other rational expression?
(Note: Please show all work so that I can understand your logic. Thank you.)
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
1.
is a rational polynomial expression,
with the polynomial as the numerator,
and the polynomial as the denominator.
It is undefined when .
For those having qualms about calling a polynomial,
we could use a fancier denominator, and write something like
(probably a safer choice),
or even (which is not equivalent to , unless you specify "except for ", so you cannot simplify).

is a rational polynomial expression,
with the polynomial as the numerator,
and the polynomial as the denominator.
It is undefined when , and when .
For those having qualms about calling a polynomial,
we could use a fancier denominator, and write something like
.

For a common denominator,
we need to include in that common denominator all the factors of the two denominators.
So, the common denominator would be
.
To get equivalent rational expression, we need to multiply numerator and denominator times the same factor(s).
So,
is equivalent to .
is equivalent to .
is equivalent to .
is equivalent to .
is equivalent to .

2. IF is an expression defined for all values of ,
which means that has no real solution, AND
IF has no real solution either,
and are "safe" to use as denominators.
Then, multiplying times will yield

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SOLUTION: 1. Create two different rational polynomial expressions with the following constraints: �one expression is undefined when x = 4, �the other is undefined when x = &#8210;2 or 0.

SOLUTION: 1. Create two different rational polynomial expressions with the following constraints: �one expression is undefined when x = 4, �the other is undefined when x = ‒2 or 0.